The present invention is directed to a method of producing a container such as a catalytic converter for holding a fragile substrate in a cylindrical housing with a shock absorbent member wrapped around the substrate, with an appropriate holding force determined on the basis of frictional force between the shock absorbent member and the one with the smaller coefficient of friction out of the substrate and the cylindrical housing. The method comprises the steps of (1) inserting the substrate with the shock absorbent member wrapped around the substrate, into the cylindrical housing loosely, (2) applying an axial load to the substrate so as to move the substrate along a longitudinal axis of the cylindrical housing by a predetermined distance, monitoring the axial load applied to the substrate, and (3) reducing a diameter of at least a part of the cylindrical housing with the substrate held therein along the longitudinal axis of the cylindrical housing, with the shock absorbent member being compressed, to such an extent that the axial load equals a predetermined value.